Vibration analysis of cross-ply laminated truncated conical shells using a spline method

Free vibration of symmetric and antisymmetric cross-ply composite laminated truncated conical shells using the spline function technique is studied. The equilibrium equations for a truncated conical shells are formulated including first-order shear deformation theory. The equations of motion are derived in terms of displacement functions and rotational functions using stress–strain and strain–displacement relationships. The coupled differential equations are solved using Bickley-type splines to obtain the generalized eigenvalue problem by combining suitable boundary conditions. The convergence and comparative results are presented. Both symmetric and anti-symmetric cross-ply shells are considered using various types of material properties. Parametric studies are made to investigate the effect of transverse shear deformation on the frequency parameter with respect to the thickness ratio, length ratio, cone angle, and circumferential mode number using different numbers of layers under various types of boundary conditions.